实值随机变量的随机序与对偶随机序

本文讨论随机变量的高阶序问题，1简要地叙述了随机变量排序的经济学含义，主要是期望效用理论与其对偶理论，2讨论了实值随机变量基于分布函数的高阶序问题，给出了其基于期望效用理论的刻画。3讨论的是实值随机变量的基于对偶理论（对偶矩)的高阶序问题，并给出了其基于随机变量的Yarri等价性度量的刻画。     

HDMRL寿命分布类

引言寿命分布类的研究在系统可靠性的估计.可靠性统计理论,策略选择以及经济模型中都有重要的作用.已知的分布类有IFR,甘RA,NBU,NBUE,DMRL,丑双BUE,砚l)VRL,以及NDVRL类等等.对偶类有DPR系列.     

关于次序统计量广义TTT序的几个结果

研究了次序统计量在广义TTT变换序(TTT变换序)和剩余财富序下的性质. 讨论了寿命分布类NBUT在增凹变换下的封闭性以及NWUT寿命分布在次序统计量下的特征.     

几种新寿命分布类

本文在前人研究的寿命分布类的基础上，给出了几种新的寿命分布类的定义，并研究了其有关的性质(主要是封闭性质)．     

序进应力加速寿命试验的Bayes推断

本文将根据序进应力加速寿命试验的数据，利用Ｂａｙｅｓ方法，探讨对有关参数，和剩余寿命分布的统计推断。     

连续广义框架及其对偶的刻画,冗余及扰动

利用算子方法研究连续广义框架及其对偶的一些性质.首先给出连续广义框架及其对偶的算子刻画;证明在合适的条件下在一个给定连续广义框架的基础上去掉部分元素后剩余的部分还能构成连续广义框架;最后得到连续广义框架及其对偶的一些扰动结果.     

一般偏差右删失数据下剩余寿命分位数回归

剩余寿命是刻画个体预期寿命的一个重要度量,对剩余寿命的早期研究主要集中在剩余均值上.然而当总体生存函数偏态或厚尾时剩余均值函数可能不存在,因此统计学者建议用剩余寿命分位数来刻画预期寿命.在完全数据和右删失数据下,剩余寿命分位数的建模和理论已经很完善.但是,在实际的调查研究中经常会遇到偏差抽样数据.例如,临床医学中的左截断数据,流行病学中的病例队列抽样数据,医学大型队列研究中的长度偏差抽样数据等等.忽略抽样偏差会导致参数估计有偏和不合理的推断结果.本文考虑一般偏差右删失数据下剩余寿命分位数回归的统计推断问题.首先,我们提出了一个一般偏差右删失数据下的剩余寿命分位数回归模型,并利用一般估计方程方法对模型中的参数进行了估计.针对已有文献常用的删失变量与协变量独立性假设,本文重点考虑了删失变量依赖于协变量场合.其次,由于估计量的渐近方差中涉及非参密度函数,在估计渐近方差时,本文采用Bootstrap方法.最后,数值模拟显示本文提出的方法有限样本性质表现很好.     

特殊关联系统下寿命的封闭性

§1.引言由同一寿命分布类■中的元件组成的关联系统(coherent system),其寿命是否仍属于(?),是可靠性数学中的一个重要问题.见 Barlow 和 Proschan(1975),Klefsj(o|¨)(1982)等.虽然在许多寿命分布类中对构成关联系统是不封闭的,如对 IFR 类,但是,一些特殊的系统,在适当的条件下,其封闭性仍然是成立的.例如,由独立同分布部件组成的 k-n(F)系统,若部件有 IFR 分布,则系统寿命亦属于 IFR 类.Klefsj(o|¨)(1984)对 NBU 类证明了并联系统的封闭性.同时,他提到在部件独立同分布时,并联系统的寿命对 NBUE,DMRL 及 HNBUE 类是否封闭的问题至今仍未解决.这篇短文对 NBUE 及 DMRL 的封闭性给出了证明,而对 HNBUE 的情形有反例说明不封闭.     

年龄点t0之后的NBU性的非参数检验方法

NBU＊t0寿命分布中新元件的寿命随机地大于旧的年龄不小于t0的元件的剩余寿命,这为更广泛地模拟元件的老化和劣化现象提供了丰富的内容。本文首先对那些t0年龄点之后剩余寿命随机等于新元件寿命的元件的结构加以刻画,然后建立了一个非参数检验方法以区分这种随机等价性和t0年龄点后的严格的NBU性,并给出了针对一个NBU＊t0但非NBU的寿命分布的例子的数值模拟结果。     

NBU(2)性的偏序刻画

为刻画同一寿命分布类中两个不同分布的NBU(2)性的强弱,本文定义了一个新的偏序,即NBU(2)序,并证明NBU(2)序具有反身性,反对称性和传递性.另外,该偏序与超可加序、NBUE序,增凹序的关系也作了探讨.基于被比较分布是指数的情况,还建立了判定NBU(2)序的一个充要条件.     

Aging properties of the residual life length of k‐out‐of‐n systems with independent but non‐identical components

The k‐out‐of‐n structure is a very popular type of redundancy in fault‐tolerant systems, it has founded wide applications in industrial and military systems during the past several decades. This paper will investigate the residual life length of a k‐out‐of‐n system with independent (not necessarily identical) components, given that the (n?k)th failure has occurred at time t?0. Behaviour of PF₂, IFR, DRHR, DMRL, NBU(2) and NBUC classes of life distributions are derived in terms of the monotonicity of the residual life given the time of the (n?k)th failure. Copyright © 2004 John Wiley & Sons, Ltd.     

随机时间剩余寿命的分布类性质

得出了随机时间剩余寿命XY的随机比较性质和矩不等式．当Y是指数分布时求出了XY的故障率的界．     

Relations among univariate aging, bivariate aging and dependence for exchangeable lifetimes

For a couple of lifetimes (X₁,X₂) with an exchangeable joint survival function , attention is focused on notions of bivariate aging that can be described in terms of properties of the level curves of . We analyze the relations existing among those notions of bivariate aging, univariate aging, and dependence. A goal and, at the same time, a method to this purpose is to define axiomatically a correspondence among those objects; in fact, we characterize notions of univariate and bivariate aging in terms of properties of dependence. Dependence between two lifetimes will be described in terms of their survival copula. The language of copulæ turns out to be generally useful for our purposes; in particular, we shall introduce the more general notion of semicopula. It will be seen that this is a natural object for our analysis. Our definitions and subsequent results will be illustrated by considering a few remarkable cases; in particular, we find some necessary or sufficient conditions for Schur-concavity of , or for IFR properties of the one-dimensional marginals. The case characterized by the condition that the survival copula of (X₁,X₂) is Archimedean will be considered in some detail. For most of our arguments, the extension to the case of n>2 is straightforward.     

更新过程中的几个随机比较结果

本文研究了更新过程中的几个随机比较结果.通过对不同时刻之前的最后一次更新发生时刻变量在失效率序、反向失效率序和似然比序意义下的随机比较,获得了若底分布F是IFR,则t之前最后一次更新的发生时刻变量SN(t)在失效率序和反向失效率序意义下关于t单调递增;若底分布F是IFR且绝对连续,则SN(t)在似然比序意义下关于t单调递增.     

Matroid basis graphs. II

Several graph-theoretic notions applied to matroid basis graphs in the preceding paper are now tied more specifically to aspects of matroids themselves. Factorizations of basis graphs and disconnections of neighborhood subgraphs are related to matroid separations. Matroids are characterized whose basis graphs have only one or two of the three types of common neighbor subgraphs. The notion of leveling is generalized and related to matroid sums, minors, and duals. Also, the problem of characterizing regular and graphic matroids through their basis graphs is discussed. Throughout, many results are obtained quite easily with the aid of certain pseudo-combivalence systems of 0–1 matrices.     

Subspaces of L(H) That Are *-Invariant

A result of Choi and Effros says how *-invariant spaces of bounded operators on Hilbert space that contain the identity can be abstractly characterized in terms of their order structure. The aim here is to dispose of the identity and to prove a similar theorem for spaces of bounded operators that are merely *-invariant. Absence of a unit will also permit to deal with duals in a satisfactory way.     

Characterizations of bipartite and Eulerian partial duals of ribbon graphs

Huggett and Moffatt characterized all bipartite partial duals of a plane graph in terms of all-crossing directions of its medial graph. Then Metsidik and Jin characterized all Eulerian partial duals of a plane graph in terms of semi-crossing directions of its medial graph. Plane graphs are ribbon graphs with genus 0. In this paper, by introducing the notion of modified medial graphs and using their all-crossing directions, we first extend Huggett and Moffatt’s result from plane graphs to ribbon graphs. Then we characterize all Eulerian partial duals of any ribbon graph in terms of crossing-total directions of its medial graph, which are simpler than semi-crossing directions.     

On the weak IFR aging of bivariate lifetime distributions

A new notion of bivariate aging in a competitive risk framework is introduced. Aging properties of bivariate distributions are defined by aging properties of a series system with possibly dependent components. A case of exponential marginals is considered. Sufficient conditions for a weak IFR aging (weak DFR negative aging) are derived and a number of simple examples are considered. Copyright © 2005 John Wiley & Sons, Ltd.     

Duality for multimodules

Suitable duals of multimodules are introduced and used to provide transposition contravariant right semi-adjunctions (and dualitites under reflexivity). Several additional notions on multimodules are discussed: generalized morphisms and involutions; tensor products and contractions; inner products; first-order differential operators. A construction of an (involutive) colored properad of multimodules is suggested.     

On a constructive approach to optimality conditions for convex SIP problems with polyhedral index sets

In the paper, we consider a problem of convex Semi-Infinite Programming with an infinite index set in the form of a convex polyhedron. In study of this problem, we apply the approach suggested in our recent paper [Kostyukova OI, Tchemisova TV. Sufficient optimality conditions for convex Semi Infinite Programming. Optim. Methods Softw. 2010;25:279–297], and based on the notions of immobile indices and their immobility orders. The main result of the paper consists in explicit optimality conditions that do not use constraint qualifications and have the form of criterion. The comparison of the new optimality conditions with other known results is provided.